All other orphans in the series lived with relatives - Harry Potter with the Dursleys, Neville Longbottom (I consider him an orphan, though his parents aren't dead yet) with his Gran, and Teddy Lupin with Andromeda Tonks. Therefore, I'm under the impression that customarily wizarding orphans are simply taken in by other living relations. But if there happen to be no living relatives, then an orphan might be left with some legal guardian, like a godfather like Sirius Black for Harry (if he hadn't gone to Azkaban) or Harry for Teddy. Or if not that, then somebody could just adopt the child.